On the rigidity of k-step nilpotent graph Lie algebras
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911297428258816 |
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| author | Barrionuevo, Josefina Tirao, Paulo |
| author_facet | Barrionuevo, Josefina Tirao, Paulo |
| contents | We thoroughly explore the class of k-step nilpotent Lie algebras associated with a simple graph looking for k-step nilpotent Lie algebras which are rigid in the variety of at most k-step nilpotent Lie algebras. We find out that, besides the complete graph, the only examples arise for k=2 and graphs of at most 4 vertices.
A key tool to prove non-k-rigidity in this context, is a general construction of non-trivial deformations for naturally graded nilpotent Lie algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04063 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the rigidity of k-step nilpotent graph Lie algebras Barrionuevo, Josefina Tirao, Paulo Rings and Algebras 17B30, 17B99 We thoroughly explore the class of k-step nilpotent Lie algebras associated with a simple graph looking for k-step nilpotent Lie algebras which are rigid in the variety of at most k-step nilpotent Lie algebras. We find out that, besides the complete graph, the only examples arise for k=2 and graphs of at most 4 vertices. A key tool to prove non-k-rigidity in this context, is a general construction of non-trivial deformations for naturally graded nilpotent Lie algebras. |
| title | On the rigidity of k-step nilpotent graph Lie algebras |
| topic | Rings and Algebras 17B30, 17B99 |
| url | https://arxiv.org/abs/2507.04063 |